IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v98y2023i2d10.1007_s00186-023-00834-z.html
   My bibliography  Save this article

Risk filtering and risk-averse control of Markovian systems subject to model uncertainty

Author

Listed:
  • Tomasz R. Bielecki

    (Illinois Institute of Technology)

  • Igor Cialenco

    (Illinois Institute of Technology)

  • Andrzej Ruszczyński

    (Rutgers University)

Abstract

We consider a Markov decision process subject to model uncertainty in a Bayesian framework, where we assume that the state process is observed but its law is unknown to the observer. In addition, while the state process and the controls are observed at time t, the actual cost that may depend on the unknown parameter is not known at time t. The controller optimizes the total cost by using a family of special risk measures, called risk filters, that are appropriately defined to take into account the model uncertainty of the controlled system. These key features lead to non-standard and non-trivial risk-averse control problems, for which we derive the Bellman principle of optimality. We illustrate the general theory on two practical examples: clinical trials and optimal investment.

Suggested Citation

  • Tomasz R. Bielecki & Igor Cialenco & Andrzej Ruszczyński, 2023. "Risk filtering and risk-averse control of Markovian systems subject to model uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(2), pages 231-268, October.
    • Handle: RePEc:spr:mathme:v:98:y:2023:i:2:d:10.1007_s00186-023-00834-z
    DOI: 10.1007/s00186-023-00834-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-023-00834-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-023-00834-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Nicole Bäuerle & Ulrich Rieder, 2014. "More Risk-Sensitive Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 105-120, February.
    2. Georg Ch Pflug & Werner Römisch, 2007. "Modeling, Measuring and Managing Risk," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6478, September.
    3. Bäuerle, Nicole & Rieder, Ulrich, 2017. "Zero-sum risk-sensitive stochastic games," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 622-642.
    4. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath & Hyejin Ku, 2007. "Coherent multiperiod risk adjusted values and Bellman’s principle," Annals of Operations Research, Springer, vol. 152(1), pages 5-22, July.
    5. Marco Frittelli & Giacomo Scandolo, 2006. "Risk Measures And Capital Requirements For Processes," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 589-612, October.
    6. Patrick Cheridito & Michael Kupper, 2011. "Composition Of Time-Consistent Dynamic Monetary Risk Measures In Discrete Time," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 137-162.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Feb 2021.
    2. Acciaio, Beatrice & Föllmer, Hans & Penner, Irina, 2012. "Risk assessment for uncertain cash flows: model ambiguity, discounting ambiguity, and the role of bubbles," LSE Research Online Documents on Economics 50118, London School of Economics and Political Science, LSE Library.
    3. Karl-Theodor Eisele & Michael Kupper, 2016. "Asymptotically stable dynamic risk assessments," Post-Print hal-03548963, HAL.
    4. Zachary Feinstein & Birgit Rudloff, 2018. "Time consistency for scalar multivariate risk measures," Papers 1810.04978, arXiv.org, revised Nov 2021.
    5. Georg Ch. Pflug & Alois Pichler, 2016. "Time-Consistent Decisions and Temporal Decomposition of Coherent Risk Functionals," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 682-699, May.
    6. Daniel Bartl, 2016. "Conditional nonlinear expectations," Papers 1612.09103, arXiv.org, revised Mar 2019.
    7. Ricardo Collado & Dávid Papp & Andrzej Ruszczyński, 2012. "Scenario decomposition of risk-averse multistage stochastic programming problems," Annals of Operations Research, Springer, vol. 200(1), pages 147-170, November.
    8. Marlon Moresco & M'elina Mailhot & Silvana M. Pesenti, 2023. "Uncertainty Propagation and Dynamic Robust Risk Measures," Papers 2308.12856, arXiv.org, revised Feb 2024.
    9. Yanhong Chen & Zachary Feinstein, 2022. "Set-valued dynamic risk measures for processes and for vectors," Finance and Stochastics, Springer, vol. 26(3), pages 505-533, July.
    10. Sıtkı Gülten & Andrzej Ruszczyński, 2015. "Two-stage portfolio optimization with higher-order conditional measures of risk," Annals of Operations Research, Springer, vol. 229(1), pages 409-427, June.
    11. Eisele Karl-Theodor & Kupper Michael, 2016. "Asymptotically stable dynamic risk assessments," Statistics & Risk Modeling, De Gruyter, vol. 33(1-2), pages 41-50, September.
    12. Tomasz R. Bielecki & Igor Cialenco & Andrzej Ruszczy'nski, 2022. "Risk Filtering and Risk-Averse Control of Markovian Systems Subject to Model Uncertainty," Papers 2206.09235, arXiv.org.
    13. Wayne King Ming Chan, 2015. "RAROC-Based Contingent Claim Valuation," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2015, January-A.
    14. Karl-Theodor Eisele & Michael Kupper, 2013. "Asymptotically Stable Dynamic Risk Assessments," Working Papers of LaRGE Research Center 2013-04, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    15. Stadje, M.A. & Pelsser, A., 2014. "Time-Consistent and Market-Consistent Evaluations (Revised version of 2012-086)," Discussion Paper 2014-002, Tilburg University, Center for Economic Research.
    16. Jingnan Fan & Andrzej Ruszczyński, 2018. "Risk measurement and risk-averse control of partially observable discrete-time Markov systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 161-184, October.
    17. Engsner, Hampus & Lindskog, Filip & Thøgersen, Julie, 2023. "Multiple-prior valuation of cash flows subject to capital requirements," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 41-56.
    18. Andrzej Ruszczynski & Jianing Yao, 2017. "A Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuation," Papers 1701.06234, arXiv.org, revised Aug 2020.
    19. Naomi Miller & Andrzej Ruszczyński, 2011. "Risk-Averse Two-Stage Stochastic Linear Programming: Modeling and Decomposition," Operations Research, INFORMS, vol. 59(1), pages 125-132, February.
    20. Tomasz Kosmala & Randall Martyr & John Moriarty, 2023. "Markov risk mappings and risk-sensitive optimal prediction," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(1), pages 91-116, February.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:98:y:2023:i:2:d:10.1007_s00186-023-00834-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.